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Algebra

6 Algebra Questions: Equations

1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients. 2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form. 3.Determine the equation of the line th

Convergence of Sequence and Proof

See attached file for full problem description. Use the definition of convergence of a sequence to prove that the sequence (n-1)/(n+2) (n=1 to infinity) converges to 1. Please provide complete proof and explanation.

Asymptotic Behavior of Solution

Use the phase line to predict the asymptotic (*see attachment*) behavior of the solution satisfying the specified initial condition ... *Please see attachment for complete question.

Symmetry : Symmetries of a Square

Please see the attached file for the fully formatted problems. ? Let S be a square, with vertices labelled (anticlockwise), 1,2,3,4. a symmetry of S is a rotation or reflection which preserves the square (although it may change the position of the vertices). Note that a symmetry is determined by its effect on the vertices.

Word Problem

A 20-foot board is cut into two pieces, Twice the length of the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

Unit conversion

An M&M has a volume of approximately 0.5 cm3. We have Avagadro's number of M&M's. The only place to store the M&M's in in Death Valley. The area of Death Valley is approximately 100miles2. How thick in miles would the layer of M&M's be?

Quadratic equation

4.76x^2 + 6.12x = -55.3 Find all real solutions, however i am getting a negative number, which is not workable?

Quadratic

I am supposed to find all real solutions: 1.5x^2 - 6.3x - 10.1 = 0 I am stuck, please see attachment

Graph the equation

Can't figure out how to solve: x^2 + y^2 + 4y = 0 I need to graph the equation in a xy coordinate system.

Surface area of a right circular cylinder

The surface area of a right circular cylinder is given by the formula S= 2*PIE SIGN*rh + 2*PIE SIGN* r^2, where r is the radius of the base, and h is the height of the cylinder. Solve the formula S= 2*PI*rh + 2*PI*r^2 for h.

Comlpex 4.3.6 with theorem.

Although Corollary 2 does not apply to the function 1 / (z — z_0) in the plane punctured at z_0, Theorem 6 can be used as follows to show that (see attached 1) for any circle C traversed once in the positive direction surrounding the point z_0. Introduce a horizontal branch cut from z_0 to infinity as in Fig. 4.25. In the r

Word problem

One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

Volume of a box

An open box with a square base is to be built for $48. The sides of the box will cost $3 per square meter, and the base will cost $4 per square meter. Express the volume of the box as a function of the length of its base.

Fibonacci Sequence

Let F be the Fibonacci sequence n F = 1, F =1 0 1 F + F n-1 n-2 show 1) For all of n, F = (7/4) ^ n n 2) n+1 n+1 F = 1/√5 ((1+√5) - (1-√5) )

Linear programming investment problem

Below problem is one that I'm drawing a blank on for even setting up the equation. Any help would be greatly appreciated. Smith recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a st